Achieving large amplitude vibrations and travelling waves via parametric excitation

Parametric excitation is an efficient method to produce large vibration amplitudes under small sinusoidal excitation forces. A difficulty arises when one seeks to generate travelling waves or short wavelength vibrations. The present paper discusses optimal boundary-conditions that amplify the parametrically excited vibration even when these exhibit short spatial wavelengths. Parametric excitation is also employed to produce travelling waves in an elastic ring where it is shown that large amplitude travelling square waves can be effectively generated on string like devices. The method is analysed analytically, numerically with partly with an experimental rig.